Charged Lepton Corrections Research Articles

Neutrino Mixing Sum Rules and the Littlest Seesaw

In this work, we study the neutrino mixing sum rules arising from discrete symmetries and the class of Littlest Seesaw (LS) neutrino models. These symmetry-based approaches all offer predictions for the cosine of the leptonic CP phase cosδ in terms of the mixing angles, θ13, θ12, θ23, while the LS models also predict the sine of the leptonic CP phase sinδ, as well as making other predictions. In particular, we study the solar neutrino mixing sum rules, arising from charged lepton corrections to tri-bimaximal (TB), bimaximal (BM), golden ratio (GR) and hexagonal (HEX) neutrino mixing, and the atmospheric neutrino mixing sum rules, arising from preserving one of the columns of these types of mixing—for example, the first or second column of the TB mixing matrix (TM1 or TM2)—and we confront them with an up-to-date global fit of the neutrino oscillation data. We show that some mixing sum rules, such as an atmospheric neutrino mixing sum rule arising from a version of neutrino golden ratio mixing (GRa1), are already excluded at 3σ, and we determine the remaining models allowed by the data. We also consider the more predictive LS models (which obey the TM1 sum rules and offer further predictions) based on constrained sequential dominance CSD(n) with n≈3. We compare for the first time the three cases n=2.5, n=3 and n=1+6≈3.45, which are favored by theoretical models, using a new type of analysis to accurately predict the observables θ12, θ23 and δ. We study all the above approaches, solar and atmospheric mixing sum rules and LS models, together so that they may be compared and to give an up-to-date analysis of the predictions of all of these possibilities, when confronted with the most recent global fits.

Predictions for the leptonic Dirac CP-violating phase

In this paper, we explore the theoretical constraints on the observable parameters of neutrino mixing on predictions for the leptonic Dirac CP-violating phase within a well-studied class of simple theoretical models that includes a single source of CP violation due to charged lepton corrections. The approach guarantees that a physically meaningful prediction for the most likely values for the leptonic Dirac CP-violating phase is obtained.

μ − τ reflection symmetry in the standard parametrization and contributions from charged lepton sector

The μ−τ reflection symmetry of the lepton mixing matrix accommodates maximal atmospheric mixing (θ23=π/4) as well as maximal Dirac CP phase (δ=±π/2) for the Dirac case. In the standard parametrization of the PMNS matrix the reflection symmetric nature is not directly visible while substituting the maximal values of the mixing parameters. This issue has been addressed in this paper. It is found that the reflection symmetry in the ‘standard’ PMNS matrix can be restored by allowing maximal values of the Majorana CP phases (α, β) as well, along with maximal δ. To accommodate non-maximal values of θ23 and δ we consider charged lepton contributions to the neutrino mixing and implement the proposed scheme of reflection symmetry in the neutrino mixing matrix. The charged lepton correction scheme succeeds in the prediction of lepton mixing parameters consistent with the global 3ν oscillation data.

Predictions for the Dirac CP -violating phase from sum rules

We explore the implications of recent results relating the Dirac CP-violating phase to predicted and measured leptonic mixing angles within a standard set of theoretical scenarios in which charged lepton corrections are responsible for generating a non-zero value of the reactor mixing angle. We employ a full set of leptonic sum rules as required by the unitarity of the lepton mixing matrix, which can be reduced to predictions for the observable mixing angles and the Dirac CP-violating phase in terms of model parameters. These sum rules are investigated within a given set of theoretical scenarios for the neutrino sector diagonalization matrix for several known classes of charged lepton corrections. The results provide explicit maps of the allowed model parameter space within each given scenario and assumed form of charged lepton perturbations.

Common origin of nonzero θ13 and dark matter in an S4 flavor symmetric model with inverse seesaw mechanism

We study an inverse seesaw model of neutrino mass within the framework of $S_4$ flavour symmetry from the requirement of generating non-zero reactor mixing angle $\theta_{13}$ along with correct dark matter relic abundance. The leading order $S_4$ model gives rise to tri-bimaximal type leptonic mixing resulting in $\theta_{13}=0$. Non-zero $\theta_{13}$ is generated at one loop level by extending the model with additional scalar and fermion fields which take part in the loop correction. The particles going inside the loop are odd under an in-built $Z^{\text{Dark}}_2$ symmetry such that the lightest $Z^{\text{Dark}}_2$ odd particle can be a dark matter candidate. Correct neutrino and dark matter phenomenology can be achieved for such one loop corrections either to the light neutrino mass matrix or to the charged lepton mass matrix although the latter case is found to be more predictive. The predictions for neutrinoless double beta decay is also discussed and inverted hierarchy in the charged lepton correction case is found to be disfavoured by the latest KamLAND-Zen data.

Modulated bimaximal neutrino mixing

The present article is an endeavor to look into some fruitful frameworks based on "Bi-maximal" neutrino mixing, from a model independent stand. The possibilities involving the correction or attenuation of the original BM mixing matrix, followed by GUT-inspired charged lepton correction are invoked. The "symmetry-basis" thus constructed, accentuates some interesting facets such as: a modified QLC relation, $\theta_{12}+\theta_{c}\approx\frac{\pi}{4}-\theta_{13}\cos(n\pi-\delta_{CP})$, a possible link up between neutrino and charged lepton sectors, $\theta_{13}^{\nu}=\theta_{12}^{l}\sim\mathcal{O}(\theta_{C})$ or that between neutrinos and quarks, $\theta_{13}^{\nu}=\theta_{C}$. The study vindicates the relevance of the Bi-maximal mixing as a first approximation.

Corrections to scaling neutrino mixing: Non-zero [formula omitted] and baryon asymmetry

We study a very specific type of neutrino mass and mixing structure based on the idea of Strong Scaling Ansatz (SSA) where the ratios of neutrino mass matrix elements belonging to two different columns are equal. There are three such possibilities, all of which are disfavored by the latest neutrino oscillation data. We focus on the specific scenario which predicts vanishing reactor mixing angle θ13 and inverted hierarchy with vanishing lightest neutrino mass. Motivated by several recent attempts to explain non-zero θ13 by incorporating corrections to a leading order neutrino mass or mixing matrix giving θ13=0, here we study the origin of non-zero θ13 as well as leptonic Dirac CP phase δCP by incorporating two different corrections to scaling neutrino mass and mixing: one, where type II seesaw acts as a correction to scaling neutrino mass matrix and the other, with charged lepton correction to scaling neutrino mixing. Although scaling neutrino mass matrix originating from type I seesaw predicts inverted hierarchy, the total neutrino mass matrix after type II seesaw correction can give rise to either normal or inverted hierarchy. However, charged lepton corrections do not disturb the inverted hierarchy prediction of scaling neutrino mass matrix. We further discriminate between neutrino hierarchies, different choices of lightest neutrino mass and Dirac CP phase by calculating baryon asymmetry and comparing with the observations made by the Planck experiment.

Search for possible forms of neutrino mixing matrix [formula omitted

Two popular forms of neutrino mixing matrix UPMNS, are the Bi-maximal (BM) mixing and Tri-bimaximal (TBM) mixing matrices which are derived from well known underlying symmetry principles. In the present work, we examine their validity after taking appropriate charged lepton corrections. Tri-bimaximal mixing matrix with charged lepton correction, agrees with the present observational data at 1σ level, but the Bi-maximal mixing with charged lepton correction, fails to accommodate the present observational data at 1σ level on neutrino oscillations. This shortcoming is removed in Bi-large (BL) mixing ansatz with appropriate charged lepton correction. We also discuss the Quark–Lepton Complementarity(QLC) relations and other related issues in neutrino physics.

Reducing [formula omitted] to 9°

We propose to consider the possibility that the observed value of θ13 is not the result of a correction from an initially vanishing value, but rather the result of a correction from an initially larger value. As an explicit example of this approach, we consider analytically and numerically well-known CKM-like charged lepton corrections to a neutrino diagonalization matrix that corresponds to a certain mixing scheme. Usually this results in generating θ13=9° from zero. We note here, however, that 9 is not only given by 0+9, but also by 18−9. Hence, the extreme case of an initial value of 18 degrees, reduced by charged lepton corrections to 9 degrees, is possible. For some cases under study, new sum rules for the mixing parameters, and correlations with CP phases, are found.

New frontiers in neutrino physics

The origin of neutrino masses and mixings is an important topic in high energy physics. In the present work, two mixing schemes namely Bi-maximal (BL) and Tri-bimaximal (TBM) mixings which are derived from μ–τ symmetric neutrino mass matrix, are examined after taking corrections from charged lepton sector. While tri-bimaximal mixing with appropriate charged lepton correction, is in good agreement with latest observations, the Bi-maximal mixing after taking charged lepton correction, fails to agree completely with observation. A new scheme called strict Bi-large (BL) mixing scheme is introduced in place of BM mixing scheme.The BL scheme works very well in complete agreement with data. Some of the unsettled issues in neutrino physics are outlined for further investigations.

Bi-large neutrino mixing with charged lepton correction

Usual bi-maximal neutrino mixing faces an inherent problem in lowering the solar angle below $$\tan^{2}\theta_{12}=0.50$$ when charged lepton correction is considered. This minimum θ 12 is achievable only if charged parity violation is absent. We start with a new model which incorporates a new idea of mixing developed recently, called bi-large mixing, similar to bi-maximal mixing except that the former chooses rather θ 13 as Cabibbo angle (θ c ) than zero. The bi-large mixing may be visualized in the framework of bi-trimaximal mixing which is related to a discrete flavour symmetry group $$\Updelta(96)$$ . Also the motivation comes from F-Theory inspired Grand unified theory. We apply this mixing in the neutrino sector followed by a charged lepton correction with the Cabibbo–Kobayashi–Maskawa type matrix, U eL . The model marks a prediction on θ 23 to lie within the first octant. The charged-parity violating phase appearing from charged lepton sector δ 12 dictates the prediction of all the three mixing angles. A proper choice of δ 12 , leads to the predictions of all the three mixing angles including θ 12, to align precisely with the experimental best-fit. This close agreement thus hoists bi-large mixing as an important and promising mixing scheme, in contrast to bi-maximal or tri-bimaximal mixing as a first approximation.

Charged lepton corrections to scaling neutrino mixing

Assuming Majorana nature of neutrinos, a general expression for the charged lepton corrections to scaling neutrino mixing has been obtained in the context of three flavor neutrino oscillations. Non-zero value of the reactor mixing angle is nicely accommodated. It is noted that scaling in the effective neutrino mass matrix is equivalent to the presence of two vanishing minors corresponding to first row elements of the effective neutrino mass matrix. A value of reactor mixing angle which is fairly close to the currently measured best fit is predicted for charged lepton corrections of the order of the Cabbibo angle. We, also, present symmetry realization of such texture structures in the framework of type-I seesaw mechanism with non-diagonal charged lepton mass matrix using discrete Abelian flavor symmetry.

On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections

Two negative signs naturally appear in the Uμ1 and Uτ2 elements of the tri-bimaximal (TBM) matrix for positive values of the mixing angles θ12 and θ23. Apart from this, in other TBM matrices negative signs are shifted to other elements in each case. They account for positive as well as negative values of θ12 and θ23. We discuss the sign ambiguity in the TBM matrix and find that the TBM matrices, in fact, can be divided into two groups under certain circumstances. Interestingly, this classification of the TBM matrices is accompanied by two different μ − τ symmetric mass matrices which can separately be related to the groups. To accommodate the non-zero value of θ13 and deviate θ23 toward the first octant, we then perturb the TBM mixing ansatz with the help of charged lepton correction. The diagonalizing matrices for the charged lepton mass matrices also possess sign ambiguity and respect the grouping of the TBM matrices. They are parameterized in terms of the Wolfenstein parameter λ and satisfy the unitarity condition up to the second order in λ.

Dependence of solar mixing angle on CP violating phase δ under deviation from tri-bimaximal mixing

We deviate tri-bimaximal neutrino mixing with the help of charged lepton mixing matrix UlL which has a structure similar to that of Cabibbo–Kobayashi–Maskawa (CKM) matrix. To enter CP violating phase δ into rotation matrix, we follow a novel method discussed by Fritzsch and Xing which is different from the standard particle data group one. Under such charged lepton correction ansatz we note that \(\tan^2 \theta_{12}\) becomes dependent on δ, from where constraints on δ phase can be obtained after employing experimental range of mixing angles. To compute numerical values of mixing angles we employ Wolfenstein parameterization of CKM matrix. We discuss implication of dependence of the physical observable parameters of neutrino oscillation on the choice of type of parameterization of the matrix.

SpontaneousCPviolation inA4×SU(5)with constrained sequential dominance 2

We revisit a two right-handed neutrino model with two texture zeros, namely an indirect model based on ${A}_{4}$ with the recently proposed new type of constrained sequential dominance (CSD2), involving vacuum alignments along the $(0,1,\ensuremath{-}1{)}^{T}$ and $(1,0,2{)}^{T}$ directions in flavor space, which are proportional to the neutrino Dirac mass matrix columns. In this paper we construct a renormalizable and unified indirect ${A}_{4}\ifmmode\times\else\texttimes\fi{}SU(5)$ model along these lines and show that, with spontaneous $CP$ violation and a suitable vacuum alignment of the phases, the charged lepton corrections lead to a reactor angle in good agreement with results from Daya Bay and RENO. The model predicts a right-angled unitarity triangle in the quark sector and a Dirac $CP$ violating oscillation phase in the lepton sector of $\ensuremath{\delta}\ensuremath{\approx}130\ifmmode^\circ\else\textdegree\fi{}$, while providing a good fit to all quark and lepton masses and mixing angles.

Nonzero |U e3| from charged lepton corrections and the atmospheric neutrino mixing angle

After the successful determination of the reactor neutrino mixing angle \theta_13 ~ 0.16 \neq 0, a new feature suggested by the current neutrino oscillation data is a sizeable deviation of the atmospheric neutrino mixing angle \theta_23 from \pi/4. Using the fact that the neutrino mixing matrix U = U_e^\dagger U_\nu, where U_e and U_\nu result from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming that U_\nu has a i) bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to the conservation of the lepton charge L' = L_e - L_\mu - L_\tau (LC), we investigate quantitatively what are the minimal forms of U_e, in terms of angles and phases it contains, that can provide the requisite corrections to U_\nu so that \theta_13, \theta_23 and the solar neutrino mixing angle \theta_12 have values compatible with the current data. Two possible orderings of the 12 and the 23 rotations in U_e, "standard" and "inverse", are considered. The results we obtain depend strongly on the type of ordering. In the case of "standard" ordering, in particular, the Dirac CP violation phase \delta, present in U, is predicted to have a value in a narrow interval around i) \delta ~ \pi in the BM (or LC) case, ii) \delta ~ 3\pi/2 or \pi/2 in the TBM case, the CP conserving values \delta = 0, \pi, 2\pi being excluded in the TBM case at more than 4\sigma. In the addendum we discuss the implications of the latest 2013 data.

Charged lepton contributions to bimaximal and tri-bimaximal mixing for generating [formula omitted] and [formula omitted

Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle θ13=0 and the atmospheric angle tan2θ23=1. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of θ13 as well as deviations of θ12 and θ23 from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on θ13 and θ23 to assign θ13≠0 and tan2θ23<1 with the help of charged lepton corrections defined by UPMNS=Ul†Uν. We first consider Uν to be given separately by BM and TB mixing matrices and then find the possible forms of Ul such that the elements of PMNS matrix, finally yield θ13≠0 and tan2θ23<1 in agreement with latest observational data. To compute the values of mixing angles we assume the charged lepton correction to be of Cabibbo–Kobayashi–Maskawa (CKM) like. All the mixing matrices involved in the calculation satisfy the unitarity condition to leading order of expansion parameter. We also analyze both the mixing schemes in presence of Dirac CP phase and find expressions for the rephasing invariant quantity JCP which have been discussed in recent literature.

Tri-bimaximal-Cabibbo mixing

Recent measurements of the lepton mixing angle θ13 by the Daya Bay and RENO reactor experiments are consistent with the relationship θ13≈θC/2 where θC is the Cabibbo angle. We propose Tri-Bimaximal-Cabibbo (TBC) mixing, in which sinθ13=sinθC/2, sinθ23=1/2 and sinθ12=1/3. We show that TBC mixing may arise approximately from tri-bimaximal, bi-maximal or Golden Ratio neutrino mixing, together with Cabibbo-like charged lepton corrections arising from a Pati–Salam gauge group, leading to predictions for the CP-violating phase of δ≈±90°,±180°,±75°, respectively. Alternatively, we show that TBC neutrino mixing may realised accurately using the type I see-saw mechanism with partially constrained sequential right-handed neutrino dominance, assuming a family symmetry which is broken by a flavon common to quarks and neutrinos.

A Grand [formula omitted] Flavour Model

Recent results from the Daya Bay and RENO reactor experiments have measured the smallest lepton mixing angle and found it to have a value of θ13≈9°. This result presents a new challenge for the existing paradigms of discrete flavour symmetries which attempt to describe all quark and lepton masses and mixing angles. Here we propose a Supersymmetric Grand Unified Theory of Flavour based on Δ(96)×SU(5), together with a U(1)×Z3 symmetry, including a full discussion of Δ(96) in a convenient basis. The Grand Δ(96)×SU(5) Flavour Model relates the quark mixing angles and masses in the form of the Gatto–Sartori–Tonin relation and realises the Georgi–Jarlskog mass relations between the charged leptons and down-type quarks. We predict a Bi-trimaximal (not Tri-bimaximal) form of neutrino mixing matrix, which, after including charged lepton corrections with zero phase, leads to the following GUT scale predictions for the atmospheric, solar, and reactor mixing angles: θ23≈36.9°, θ12≈32.7° and θ13≈9.6°, in good agreement with recent global fits, and a zero Dirac CP phase δ≈0.

Formula omitted] from GUTs

The recent observations of the leptonic mixing angle θ13PMNS are consistent with θ13PMNS=θC/2 (with θC being the Cabibbo angle θ12CKM). We discuss how this relation can emerge in Grand Unified Theories (GUTs) via charged lepton corrections. The key ingredient is that in GUTs the down-type quark Yukawa matrix and the charged lepton Yukawa matrix are generated from the same set of GUT operators, which implies that the resulting entries are linked and differ only by group-theoretical Clebsch factors. This allows a link θ12e≈θC to be established, which can induce θ13PMNS≈θC/2 provided that the 1–3 mixing in the neutrino mass matrix is much smaller than θC. We find simple conditions under which θ13PMNS≈θC/2 can arise via this link in SU(5) GUTs and Pati–Salam models. We also discuss possible corrections to the exact relation. Using lepton mixing sum rules different neutrino mixing patterns can be distinguished by their predictions for the Dirac CP phase δPMNS.